Resonances of a non-linear s.d.o.f. system with two time-delays in linear feedback control

Abstract

The primary, superharmonic, and subharmonic resonances of a harmonically excited non-linear s.d.o.f. system with two distinct time-delays in the linear state feeback are studied. The two different time-delays are presented in the proportional feedback and the derivative feedback respectively. The method of multiple scales is utilized to obtain the first order approximation of response. The effect of the feedback gains and time-delays on the steady state responses of three types of resonances is investigated. It is found that a proper selection of the feedback gains and time-delays can enhance the control performance.